Question

Basic Electricity - voltage current relationship of passive elements for different input signals

Answer 1

Passive electrical elements, such as resistors, capacitors, and inductors, exhibit different relationships between voltage and current when subjected to different types of input signals. Let's explore these relationships for different types of input signals: DC (direct current), AC (alternating current), and transient signals.

DC (Direct Current):
In the case of a DC input signal, which is a constant voltage or current, the relationships are quite simple:

Resistor (R): According to Ohm's Law (V = IR), the voltage across a resistor is directly proportional to the current flowing through it. The resistance determines the ratio between voltage and current.

Capacitor (C): In the presence of a DC signal, a capacitor acts as an open circuit (effectively blocking the flow of current after it's initially charged). Therefore, the voltage across a capacitor can change instantaneously, but there is no steady-state current flow.

Inductor (L): In the presence of a DC signal, an inductor acts as a short circuit (allowing current to flow through it). The voltage across an inductor can change instantaneously, but there is no steady-state voltage difference.

AC (Alternating Current):
AC signals continuously vary between positive and negative values, leading to more complex relationships:

Resistor (R): Ohm's Law still holds for AC signals. The voltage across a resistor is proportional to the current flowing through it, and the phase relationship is zero degrees.

Capacitor (C): In an AC circuit, a capacitor's impedance (opposition to current flow) decreases as frequency increases. The relationship between voltage and current across a capacitor is given by:

=

⋅




I=C⋅
dt
dV
    ​

, where

I is the current,

C is the capacitance, and




dt
dV
    ​

 represents the rate of change of voltage with respect to time. The phase relationship is a leading phase of -90 degrees, meaning that the current leads the voltage by 90 degrees.

Inductor (L): An inductor's impedance increases with frequency. The relationship between voltage and current across an inductor is given by:

=

⋅




V=L⋅
dt
dI
    ​

, where

V is the voltage,

L is the inductance, and




dt
dI
    ​

 represents the rate of change of current with respect to time. The phase relationship is a lagging phase of +90 degrees, meaning that the voltage lags behind the current by 90 degrees.

Transient Signals:
Transient signals are sudden changes or disturbances in an electrical circuit. They can trigger various responses in passive elements:

Resistor (R): A resistor responds instantaneously to changes in voltage or current, and there are no specific phase relationships in transient responses.

Capacitor (C): When a sudden voltage change is applied across a capacitor, it charges or discharges with a time constant determined by the product of resistance and capacitance (

=

⋅

τ=R⋅C). The voltage across a charging capacitor rises exponentially, while the voltage across a discharging capacitor decreases exponentially.

Inductor (L): When a sudden change in current occurs in an inductor, it induces an opposing voltage. The voltage across an inductor resists rapid changes in current, leading to a gradual increase or decrease.

Remember that these descriptions are simplifications, and real-world circuits may involve more complex interactions and considerations, especially when multiple elements are combined in a circuit.